Max-Min Ant System

In MMAS, only the best ant deposits pheromone (iteration-best or best-so-far). Furthermore, we enforce bounds to prevent premature lock-in/stagnation:

Typical updates:

$$\begin{array}{rl}{\tau }_{ij}& \leftarrow (1-\rho ){\tau }_{ij}+\Delta {\tau }_{ij}^{\text{best}}\\ {\tau }_{ij}& \leftarrow \text{min}({\tau }_{\text{max}},\text{max}({\tau }_{\text{min}},{\tau }_{ij}))\end{array}$$

This lets us explicitly control stagnation and maintain exploration.